MinT - Best Known (176, 176+47, s)-Nets in Base 2

Best Known (176, 176+47, s)-Nets in Base 2

(176, 176+47, 260)-Net over F₂ — Constructive and digital

Digital (176, 223, 260)-net over F₂, using

t-expansion [i] based on digital (174, 223, 260)-net over F₂, using
- 1 times m-reduction [i] based on digital (174, 224, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 56, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(176, 176+47, 486)-Net over F₂ — Digital

Digital (176, 223, 486)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(176, 176+47, 7552)-Net in Base 2 — Upper bound on s

There is no (176, 223, 7553)-net in base 2, because

1 times m-reduction [i] would yield (176, 222, 7553)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 745686 012039 067831 026590 031850 042154 560458 460628 311528 657862 545408 > 2²²² [i]